Let's examine Will we go? first:
Will we go?
You are in a group of people, speaking for the group, and asking the entire group if everyone in it wants to go.
It can also be a shortened form of Will we go next? - in a situation such as a group waiting their turn for an amusement park ride or similar.
Won't we go?
This is will we go in the negative (will we not go?) You are in a group of people, speaking for the group, and asking the entire group if everyone in it does not wish to go.
Sometimes questions use this negative form (auxillary verb + not) as a shallow form of indirection, "softening," or politeness. The positive form is more clear but also more direct which may not be wanted in somewhat more polite or "begging" situations:
Can't we go to the park, Dad? (used as if it were Can we go to the park, Dad?)
Haven't we done this before? (used as if it were Have we done this before?)
Shouldn't we stop doing this now? (etc...)
Wouldn't he have known that?
"Won't we go?" follows the same principle.
Similarly:
Will I leave?
You are asking someone if you are going to leave.
Typically, the stress will be on the I, meaning the speaker/writer wants to confirm he/she is the one that is going to leave.
This also may come up if the speaker/writer is discussing a plan of some sort and wants to know if he/she will leave at some determined time, the determined time being understood from the context.
Won't I leave?
As explained with won't we go, this would be an indirect, "soft", or polite form of will I leave.
They are both grammatically correct, but they mean slightly different things.
He will not (or he won't) is simply a statement about the future. It's not specific about time or anything else, and is just the simplest possible way to make the statement. For example, it might be used in the following exchange:
"Yesterday we had to throw a man out of the bar. But if he comes back, he won't get in, because I hired a bouncer to watch the door."
Never makes a stronger statement, that something will not ever be true at any time, under any circumstances. Mostly it's used for emphasis. For example,
"Roberto is applying for membership in the Explorers' Club, but he will never get in, because last year he got drunk and insulted the president's mother."
Best Answer
Won't is simply a contraction of the words will not. They have the exact same meaning. Won't is more informal; if you're writing an essay, in most cases you're advised not to use any contractions. Beyond that, there's no reason not to choose whichever you like. More often when speaking, you'll hear won't. So if you're writing dialogue, you might use the contraction to make it sound more natural.